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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 14 — Jul. 4, 2011
  • pp: 13675–13685
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Controlling cascade dressing interaction of four-wave mixing image

Changbiao Li, Yanpeng Zhang, Huaibin Zheng, Zhiguo Wang, Haixia Chen, Suling Sang, Ruyi Zhang, Zhenkun Wu, Liang Li, and Peiying Li  »View Author Affiliations


Optics Express, Vol. 19, Issue 14, pp. 13675-13685 (2011)
http://dx.doi.org/10.1364/OE.19.013675


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Abstract

We report our observations on enhancement and suppression of spatial four-wave mixing (FWM) images and the interplay of four coexisting FWM processes in a two-level atomic system associating with three-level atomic system as comparison. The phenomenon of spatial splitting of the FWM signal has been observed in both x and y directions. Such FWM spatial splitting is induced by the enhanced cross-Kerr nonlinearity due to atomic coherence. The intensity of the spatial FWM signal can be controlled by an additional dressing field. Studies on such controllable beam splitting can be very useful in understanding spatial soliton formation and interactions, and in applications of spatial signal processing.

© 2011 OSA

1. Introduction

Efficient four-wave mixing (FWM) processes enhanced by atomic coherence in multilevel atomic systems [1

1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–9999 (1997). [CrossRef]

4

4. H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009). [CrossRef]

] are of great current interest. Recently, destructive and constructive interferences in a two-level atomic system [5

5. S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007). [CrossRef] [PubMed]

] and competition via atomic coherence in a four-level atomic system [6

6. Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007). [CrossRef]

] with two coexisting FWM processes were studied. Also, the interactions of doubly dressed states and the corresponding effects of atomic systems have attracted many researchers in recent years [7

7. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999). [CrossRef]

,8

8. M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001). [CrossRef]

]. The interaction of double-dark state and splitting of a dark state in a four-level atomic system were studied theoretically in an electromagnetically induced transparency (EIT) system by Lukin et al. [7

7. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999). [CrossRef]

]. The triple-peak absorption spectrum, which was observed later in the N-type cold atomic system by Zhu et al., verified the existence of the secondarily dressed states [8

8. M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001). [CrossRef]

]. Recently, we had theoretically investigated three types of doubly dressed schemes in a five-level atomic system [9

9. Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008). [CrossRef]

] and observed three-peak Autler-Townes (AT) splitting of the secondary dressing FWM signal [10

10. Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]

]. In addition, we reported the evolution of suppression and enhancement of FWM signal by controlling an additional laser field [11

11. C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009). [CrossRef]

].

As two or more laser beams pass through an atomic medium, the cross-phase modulation (XPM), as well as modified self-phase modulation (SPM), can potentially affect the propagation and spatial patterns of the incident laser beams. Laser beam self-focusing [12

12. G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64(21), 2487–2490 (1990). [CrossRef] [PubMed]

] and pattern formation [13

13. R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud Jr, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002). [CrossRef] [PubMed]

] have been extensively investigated with two laser beams propagating in atomic vapors. Recently, we have observed spatial shift [14

14. A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. 17(1), 19–21 (1992). [CrossRef] [PubMed]

] and spatial splitting [15

15. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001). [CrossRef] [PubMed]

17

17. Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010). [CrossRef]

] of the FWM beams generated in multi-level atomic systems, which can be well controlled by additional dressing laser beams via XPM. Studies on such spatial shift and splitting of the laser beams can be very useful in understanding the formation and interactions of spatial solitons [16

16. W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998). [CrossRef]

] in the Kerr nonlinear systems and signal processing applications, such as spatial image storage [18

18. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008). [CrossRef] [PubMed]

], entangled spatial images [19

19. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef] [PubMed]

], soliton pair generation [20

20. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000). [CrossRef] [PubMed]

], and influences of higher-order (such as fifth-order) nonlinearities [21

21. Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009). [CrossRef] [PubMed]

].

In this paper, we first report our experimental studies of the interaction of four coexisting FWM processes in a two-level atomic system by blocking different laser beams. Next, we investigate the various suppression/enhancement of the degenerate-FWM (DFWM) signals and two dispersion centers, which are caused by the cascade dressing interaction of two dressing fields. The experimental results clearly show the evolutions of the enhancement and suppression, from pure enhancement to partial enhancement/suppression, then to pure suppression, further to partial enhancement/suppression, and finally to enhancement, which are in good agreement with the theoretical calculations. In addition, we also observe the spatial splitting in the x and y directions of DFWM signal due to different spatially alignment of the probe and coupling beams.

2. Theoretical model and experimental scheme

The two relevant experimental systems are shown in Figs. 1(a)
Fig. 1 (a) and (b) The diagram of relevant Na energy levels. (c) The scheme of the experiment. Inset gives the spatial alignments of the incident beams.
and 1(b). Three energy levels from sodium atom in heat pipe oven are involved in the experimental schemes. The pulse laser beams are aligned spatially as shown in Fig. 1(c). In the Fig. 1(a), energy levels |0〉 (3S1/2) and |1〉 (3P3/2) form a two-level atomic system. Coupling field E1 (with wave vector k1 and the Rabi frequency G1) together with E1 (k1 and G1) (connecting the transition between |0〉 and |1〉) having a small angle (0.3) propagates in the opposite direction of the probe field E3 (k3 and G3) (also connecting the transition between |0〉 and |1〉). These three laser beams come from the same near-transform-limited dye laser (with a 10 Hz repetition rate, 5 ns pulse width, and 0.04 cm1 linewidth) with the same frequency detuning Δ1=ω10ω1, where ω10 is the transition frequency between |0〉 and |1〉. The coupling fields E1 and E1 induce a population grating between states |0〉 to |1〉, which is probed by E3. This generates a DFWM process (Fig. 1(a)) satisfying the phase-matching condition of kF1=k1k1+k3. Then, two additional coupling fields E2 (k2, G2) and E2 (k2, G2) are applied as scanning fields connecting the transition from |0〉 to |1〉 with the same frequency detuning Δ2=ω10ω2; the two additional coupling fields are from another similar dye laser set at ω2 to dress the energy level |1〉. The fields E2, E2, and E3 produce a non-degenerate FWM (NDFWM) signal kF2 (satisfying kF2=k2k2+k3). When the five laser beams are all on, there also exist other two FWM processes kF3 (satisfying kF3=k2k1+k3) and kF4 (satisfying kF4=k1k2+k3) in the same directions as EF1 and EF2, respectively.

Under the experimental condition, E1 (or E1) with detuning Δ1 depletes two groups of atoms with different velocities at the same time, such as negative velocities group and positive velocities group. At Δ1<0, the positive velocities group will see E1 (or E1) with detuning Δ1+k1v and E3 with detuning Δ1k3v. The frequency of the DFWM EF1in this case will be ωf=(ω1kv)(ω1kv)+(ω1+k3v)=ω1+k3v due to the conservation of energy. Correspondingly, at Δ1>0, negative velocities group will see E1 (or E1) with detuning Δ1k1v and E3 with detuning Δ1+k3v. The frequency of EF1 will be ωf=(ω1+kv)(ω1+kv)+(ω1k3v)=ω1k3v. Such changing implies that a group of atoms with certain velocities can satisfy the condition Δ1=Δ1±k1v, where Δ1 is the detuning of E1 (or E1) based on both saturation excitation and atomic coherence effect. As a result, the self-dressing field E1 (or E1) can be considered as the outer dressing field and separates the level |0〉 into two dressing states |G1±>, as shown in Fig. 2
Fig. 2 (Color online) The interplay and mutual suppression/enhancement between two coexisting FWM signals (EF1 and EF3). (a1) the upper curves: pure DFWM signal EF1 (with both E2and E2 blocked) (squares), singly dressed DFWM signal EF1 (with E2 blocked) (triangles), coexisting singly dressed DFWM signal EF1 and FWM signal EF3 (with E2 blocked) (reverse triangles), and coexisting dressed DFWM signal EF1 and FWM signal EF3 (circles);lower curves: pure FWM signal EF3 (with both E1and E2 blocked) (left triangle), singly-dressed FWM signal (with E1 blocked) (right triangle); Δ1=0. The inserted plot: corresponding to the dressed-state picture. (b1) the condition are the same to that in (a1) except Δ1=25.9  GHz. The inserted plot: corresponding to the dressed-state picture. (a2) and (b2) theoretical plots corresponding to the experimental parameters of (a1) and (b1), respectively.
. In addition, the Doppler effect and the power broadening effect on the weak FWM signals need to be considered.

When E1, E1, E2, E2 and E3 are open, the DFWM process EF1and NDFWM processes EF2, EF3 and EF4 are generated simultaneously, and there exists interplay among these four FWM signals in the two-level atomic system. These generated FWM signals have the frequencies ωF1=ωF2=ω1, ωF3=ω2, and ωF4=2ω1ω2. They are split into two equal components by a 50% beam splitter before being detected. One is captured by the CCD camera, and the other is detected by photomultiplier tubes (D1 or D2) and a fast gated integrator (gate width of 50 ns). Also, they are monitored by digital acquisition card.

The experiments are carried out in a vapor cell containing sodium. The cell, 18-cm long, is heated up to a temperature of about 230C and crossed by linearly polarized laser beams which interact with the atoms. In the two-level atomic system, the coupling fields E1 and E1 (with diameter of 0.8 mm and power of 9 μW), and the probe field E3 (with diameter of 0.8 mm and power of 3 μW) are tuned to the line center (589.0 nm) of the |0 to |1 transition, which generate the DFWM signal EF1 at frequency ω1. The coupling fields E2 and E2 (with diameter of 1.1 mm and powers of 20 μW and 100 μW, respectively) are scanned simultaneously around the |0 to |1 transition to dress the DFWM process EF1.

3. Cascade dressing interaction

We first investigate the interaction of four coexisting FWM signals in the two-level atomic system by blocking different laser beams. Firstly, by blocking E2 (or E1), the DFWM signal EF1 (or the FWM signal EF3) is suppressed by the coupling field E2 as can be seen from the upper triangle points [or the right triangle points in Fig. 2(a1)], compared to the pure DFWM signal EF1 (or the FWM signal EF3). Next, when laser beams E1, E1, E2 and E3 are turned on, two coexisting FWM processes (EF1 and EF3) couple to each other (the lower triangle points), and the intensities of total FWM signals are increased, as can be attributed to the combination of two FWM signal processes (EF1 and EF3). Finally, when all the five laser beams are turned on, the DFWM signal EF1 and the FWM signal EF3 are both greatly suppressed by corresponding dressing fields. So the intensities of total FWM signals are extremely decreased, as shown in the circles points in Fig. 2(a1).

These effects can be explained effectively by the dressed-state picture. The dressing field E2 couples the transition |0> to |1> and creates the dressed states |G2±>, which leads to single-photon transition |0>|1> off-resonance [the inserted plot in Fig. 2(a1)]. At exact single-photon resonance with Δ1=0, the DFWM signal EF1 intensity is greatly suppressed by the means of scanning the dressing field E2 across the resonance (Δ2=0), as the upper triangle points in Fig. 2(a1) shows. At the same time, the FWM signal EF3 experiences similar process [the right triangle points in Fig. 2(a1)].

Furthermore, an appropriate Δ1 value at which EF1 is either enhanced or suppressed is chosen in the investigation. In this case, compared to the pure DFWM signal EF1 [square points in Fig. 2(b1)], the dressed DFWM signal EF1 is enhanced [the upper and low triangle points in Fig. 2(b1)]. However, the dressed FWM signal EF3 is suppressed due to the destructive interference [right triangle points in Fig. 2(b1)] compared to the pure signal [left triangle points in Fig. 2(b1)]. The upper triangle in Fig. 2(b1) combines the two FWM processes (EF1 and EF3), which are dressed by laser beams E1 and E2, respectively. After calculating ρF1(3) and ρF3(3) under the above experiment conditions, good agreements are obtained between the theoretical calculations and the experimental results as shown in Figs. 2(a2) and 2(b2), respectively.

After that, we investigate the evolutions of the interaction between these two coexisting FWM signals by the means of setting different frequency detuning Δ1 values, where the fixed spectra corresponds to the suppression and enhancement of DFWM signal EF1, and the shifting spectra corresponds to the FWM signal EF3 as shown in Figs. 3
Fig. 3 (a) and (b) Measured evolution of the four FWM signals [(EF1and EF3) and (EF2 and EF4), respectively] versus Δ2 for different Δ1 values. (a1)-(a7) and (b1)-(b7): Δ1=-139.1, −103.87, −29.5, 0, 29.8, 100.1, 155.7GHz, respectively.
(a1)–3(a7). It is obvious in Figs. 3(a1)–3(a3) that, as the frequency detuning Δ1 varies from Δ1<0 to zero from up to down, the DFWM signal EF1 shows the evolution from enhancement to partial enhancement/suppression, and then to suppression. At the same time, the FWM signal EF3 varies from intense to weak (when two FWM signals EF1 and EF3 overlap) and shifts from left side to right side, which satisfies the two-photon resonant condition (Δ1Δ2=0). When Δ1 changes further to be positive, a symmetric process is observed [i.e., suppression in Fig. 3(a5), partial suppression/enhancement in Fig. 3(a6), and pure enhancement in Fig. 3(a7)]. It should be noted here that FWM signal EF3 still shifts from left side to right side. Figure 3(a4) shows the weakened FWM signal due to the strong effect of the Doppler absorption. Especially, the DFWM signal EF1 at a large one-photon detuning is extremely weak when G2=0. However, the strong dressing field can cause the resonant excitation of one of the dressed states if the enhanced condition Δ1Δ2±G2=0 is satisfied. In such case, the DFWM signal EF1 is strongly enhanced [Fig. 3(a1)], mainly due to the one-photon resonance (|0>|G2+|) [the insert plot in Fig. 2(b1)]. As Δ1=0, the intensity of the DFWM signal EF1 is greatly suppressed [Fig. 3(a3)], similar to the case of the upper triangle curves in Fig. 2(a1). Also, we can observe the FWM signal EF3 is suppressed due to the destructive interference. In addition, Figs. 3(b1)–3(b7) show the interaction of another two coexisting the FWM processes (EF2 and EF4), in which the fixed spectra corresponds to the FWM signal EF2, and the shifting spectra corresponds to FWM signal EF4 for different frequency detuning Δ1 values.

Now, we concentrate on the cascade dressing interaction and the two dispersion centers of FWM images with two dressing fields E1 and E2 in the two-level atomic system. In order to investigate the cascade dressing interaction, the power of the coupling field E1 is set at 80μW. So the DFWM signal EF1 shows a spectrum of the AT splitting due to self-dressed effect [10

10. Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]

] induced by beam k1 when Δ1 is scanned and the dressing field E2 is off, as shown in the dashed curve of Fig. 4(a)
Fig. 4 (Color online) (a) Measured suppression and enhancement of DFWM signal EF1 versus Δ2 for different Δ1values in the two-level system. Δ1=-69.1, −55.5, −38.7, −19.2, 0, 14.7, 28.8, 42.2 and 57.3 GHz, respectively. The dashed curve is the double-peak DFWM signal EF1 versus Δ1. (b) Theoretical plots corresponding to the experimental parameters in (a). (c) The same measures to (a) with the same condition, except that the laser beams E1, E1 overlap in the middle of heat oven. (d1)-(d9) the dressed-state pictures of the suppression or enhancement of the DFWM signal. The states |G1±> (dashed lines) and the states |G1+±> or |G1±> (dot-dashed lines), respectively.
. When the beam k2 is on, the DFWM signal EF1 is dressed by both E1 and E2, and therefore shows the cascade dressing interaction, as shown in Figs. 4(a) and 4(c). Specifically, by discretely choosing different detuning values within Δ1<0 and scanning Δ2, the DFWM signal EF1shows the evolution of the successively occurring pure enhancement, partial suppression/enhancement, pure suppression, partial enhancement/suppression and enhancement processes, as shown in the left side of Fig. 4(a). When Δ1 changes to be positive, a symmetric process occurs, in the right side of Fig. 4(a), which is well described by the theoretical curves [Fig. 4(b)].

Specially, we observed the y-direction spatial splitting images of the DFWM signal EF1 [Fig. 5(b)] by carefully arranging laser beams k1 andk1. In the experiment, the beams E1 and E1 are deliberately aligned in y-z plane with an angle θ (0.05) to induce a grating in the same plane with the fringe spacing Λ=λ1/θ. Because θ is far less than the angle of E1 and E1 in the x-z plane, Λ is big enough for observing the splitting caused by the induced grating. Furthermore when E1and E1 are set in the middle of the oven, EF1and E1 overlap in y-direction due to the phase matching condition. As a result, the splitting of EF1 in x-direction due to the nonlinear cross-Kerr effect from E1 disappears simultaneously. Because Λ remains nearly the same for the changeless θ and λ1, a larger spot of the EF1 beam with larger intensity will be split to more parts. In Fig. 5(b), the field E3 is stronger than that in Fig. 5(a), which leads to stronger FWM signals passing through the grating in y-direction. So we can easily obtain the splitting in y-direction. Moreover, in the enhanced position, the profile of the FWM signal become larger, and more split parts induced by the grating can be obtained. Here, Figs. 5(b1)-5(b3) show the experimental spots corresponding to the curves in Figs. 4(c1)-4(c3). However, the effects of suppression and enhancement of the DFWM signal EF1 are much worse due to the special spatial alignment of the laser beams, as shown in Fig. 4(c) compared to that in Fig. 4(a). In Fig. 4(a), theE1, E1 and E2, E2 are all set at the back of the heat oven. But in Fig. 4(c), only E1and E1 are deliberately moved to the middle of the oven to demonstrate the splitting of EF1 in the y-direction. So the dressing effect on EF1 by E2 in Fig. 4(c) appears worse than that in Fig. 4(a).

In order to verify the cascade dressing interaction and two dispersion centers of FWM image. The dresses field E2 is tuned to the line center (568.8 nm) of the |1> to |2> (4D3/2,5/2) transition, and a ladder type three-level atomic system forms, as shown in Fig. 1(b). With the dressed perturbation chains, we can obtain IEF1|ρEF1(3)|2, where ρEF1(3)=iG3G1(G1)*/(B6B72), with d8=Γ00+i(Δ1+Δ2), d9=Γ21+iΔ2,d10=Γ11+A9, d11=d1+A7, A7=G22/d8, A8=G12/d11, A9=G22/d9, A10=G12/d10, B6=Γ00+A8 and B7=d1+A7+A10.

4. Conclusion

In conclusion, we have experimentally observed the suppression and enhancement of the spatial FWM signal by the controlled cascade interaction of additional dressing fields, and the corresponding controlled spatial splitting of FWM signal caused by the enhanced cross-Kerr nonlinearity due to atomic coherence in two- and three-level atomic systems. In addition, we report the interplay between the two coexisting FWM signals, which can be tuned to overlap or separate by varying frequency detunings. Such controllable FWM processes can have important applications in wavelength conversion for spatial signal processing and optical communication.

Acknowledgments

This work was supported by NSFC (10974151, 61078002, 61078020), NCET (08-0431), RFDP (20100201120031), 2009xjtujc08, xjj20100100, xjj20100151.

References and links

1.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–9999 (1997). [CrossRef]

2.

P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20(9), 982–984 (1995). [CrossRef] [PubMed]

3.

B. Lü, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping,” Opt. Lett. 23(10), 804–806 (1998). [CrossRef] [PubMed]

4.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009). [CrossRef]

5.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007). [CrossRef] [PubMed]

6.

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007). [CrossRef]

7.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999). [CrossRef]

8.

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001). [CrossRef]

9.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008). [CrossRef]

10.

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]

11.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009). [CrossRef]

12.

G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64(21), 2487–2490 (1990). [CrossRef] [PubMed]

13.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud Jr, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002). [CrossRef] [PubMed]

14.

A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. 17(1), 19–21 (1992). [CrossRef] [PubMed]

15.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001). [CrossRef] [PubMed]

16.

W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998). [CrossRef]

17.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010). [CrossRef]

18.

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008). [CrossRef] [PubMed]

19.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef] [PubMed]

20.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000). [CrossRef] [PubMed]

21.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009). [CrossRef] [PubMed]

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.4180) Nonlinear optics : Multiphoton processes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(270.1670) Quantum optics : Coherent optical effects
(300.2570) Spectroscopy : Four-wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 11, 2011
Revised Manuscript: May 21, 2011
Manuscript Accepted: June 19, 2011
Published: June 30, 2011

Citation
Changbiao Li, Yanpeng Zhang, Huaibin Zheng, Zhiguo Wang, Haixia Chen, Suling Sang, Ruyi Zhang, Zhenkun Wu, Liang Li, and Peiying Li, "Controlling cascade dressing interaction of four-wave mixing image," Opt. Express 19, 13675-13685 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13675


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References

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